Entropy and specific heat for open systems in steady states

TL;DR

This paper challenges the applicability of the Boltzmann distribution to open systems in steady states and proposes an effective Hamiltonian approach to calculate thermodynamic quantities for such systems.

Contribution

It introduces a new method using effective Hamiltonians to analyze thermodynamics of open systems in steady states, deviating from traditional Boltzmann-based assumptions.

Findings

Boltzmann distribution cannot describe steady states of open systems

Derived expressions for specific heat, free energy, and entropy using effective Hamiltonian

Illustrated the approach with specific examples

Abstract

The fundamental assumption of statistical mechanics is that the system is equally likely in any of the accessible microstates. Based on this assumption, the Boltzmann distribution is derived and the full theory of statistical thermodynamics can be built. In this paper, we show that the Boltzmann distribution in general can not describe the steady state of open system. Based on the effective Hamiltonian approach, we calculate the specific heat, the free energy and the entropy for an open system in steady states. Examples are illustrated and discussed.